Over the past decade, the field of image processing has made tremendous advances. One type of image processing that is currently of particular interest is "tomographic imaging," a technique for computing the density function of a body, or discontinuity surfaces of this function. Today, tomography is widely used, and has applications in such fields as medicine, engineering, physics, geophysics, and security. The Radon Transform and Local Tomography clearly explains the theoretical, computational, and practical aspects of applied tomography. It includes sufficient background information to make it essentially self-contained for most readers.
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6 of 7 people found the following review helpful:
1.0 out of 5 stars
There are much better books on mathematics of tomography,
By A Customer
This review is from: The Radon Transform and Local Tomography (Hardcover)
I bought this book, but found it pretty much useless. In my opinion, its presentation of techniques and the history of the subject is skewed. Authors' contributions are presented in an overinflated manner, so the reader would never guess that sometimes there exist more powerful and at the same time simpler approaches. There are much better books on mathematics of tomography, for instance the ones written by F. Natterer. Analytically inclined readers would like to read other books on Radon transform, e.g. the one by S. Helgason. The old books directed towards applications by G. Herman and Kak and Slaney are still of value. There are also some good edited volumes on the subject.
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Inside This Book
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First Sentence:
The Radon transform of a function f(x), x Rn, is defined to be Rf := f(,p) := f(x)ds, where Sn-1, Sn-1 is the unit sphere in Rn, p R, l p := {x : x = p} is a plane, and ds is the Lebesgue measure on this plane. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
pseudolocal tomography, incomplete tomographic data, tomography formula, local tomographic data, tomography function, leading singular term, limited angle data, misclassified points, finding discontinuities, plane lap, hole theorem, singular support, range theorem, following coordinate system, slice theorem, desired assertion, local equation, discontinuity curve, detected edges, inversion formula, moment conditions, intensity plot, operator adjoint, integral geometry Key Phrases - Capitalized Phrases (CAPs): (learn more)
Monte Carlo, Applying Lemma, Synthetic Aperture Radar, Using Step New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The Radon transform of a function f(x), x Rn, is defined to be Rf := f(,p) := f(x)ds, where Sn-1, Sn-1 is the unit sphere in Rn, p R, l p := {x : x = p} is a plane, and ds is the Lebesgue measure on this plane. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
pseudolocal tomography, incomplete tomographic data, tomography formula, local tomographic data, tomography function, leading singular term, limited angle data, misclassified points, finding discontinuities, plane lap, hole theorem, singular support, range theorem, following coordinate system, slice theorem, desired assertion, local equation, discontinuity curve, detected edges, inversion formula, moment conditions, intensity plot, operator adjoint, integral geometry Key Phrases - Capitalized Phrases (CAPs): (learn more)
Monte Carlo, Applying Lemma, Synthetic Aperture Radar, Using Step New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 29
books:
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10
books
cite this book:
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- Singular Integral Equations by N.I. Muskhelishvili in Back Matter
- Functional Analysis by L. V. Kantorovich in Back Matter
- Perturbation Theory for Linear Operators (Classics in Mathematics) by Tosio Kato in Back Matter
- Lectures on Integral Transforms (Translations of Mathematical Monographs) by N. I. Akhiezer in Back Matter
- Special Functions and the Theory of Group Representations (Translations of Mathematical Monographs) by N. Ja. Vilenkin in Back Matter
See all 29 books this book cites
- Einführung in die Computertomographie: Mathematisch-physikalische Grundlagen der Bildrekonstruktion (German Edition) by Thorsten M. Buzug on page 414
- Ultrasound in Food Processing by T.J. Mason on page 83
- Sampling, Wavelets, and Tomography (Applied and Numerical Harmonic Analysis) by John J. Benedetto on page 286
- Inverse Problems: Mathematical and Analytical Techniques with Applications to Engineering by Alexander G. Ramm in Back Matter
- Inverse Problems and Inverse Scattering of Plane Waves by Dilip N. Ghosh Roy on page 327
See all 10 books citing this book
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